Simple Differential Evolution Algorithm

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Description

Simple Differential Evolution for Minimization.

Usage

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simpleDE(fun, lower, upper, N = 64, nmax = 256, r = 0.4, 
            confined = TRUE, log = FALSE)

Arguments

fun

the objective function to be minimized.

lower

vector of lower bounds for all coordinates.

upper

vector of upper bounds for all coordinates.

N

population size.

nmax

bound on the number of generations.

r

amplification factor.

confined

logical; stay confined within bounds.

log

logical; shall a trace be printed.

Details

Evolutionary search to minimize a function: For points in the current generation, children are formed by taking a linear combination of parents, i.e., each member of the next generation has the form

p_1 + r(p_2 - p_3)

where the p_i are members of the current generation and r is an amplification factor.

Value

List with the following components:

fmin

function value at the minimum found.

xmin

numeric vector representing the minimum.

Note

Original Mathematica version by Dirk Laurie in the SIAM textbook. Translated to R by Hans W Borchers.

Author(s)

HwB <hwborchers@googlemail.com>

References

Dirk Laurie. “A Complex Optimization". Chapter 5 In: F. Bornemann, D. Laurie, S. Wagon, and J. Waldvogel (Eds.). The SIAM 100-Digit Challenge. Society of Industrial and Applied Mathematics, 2004.

See Also

simpleEA, DEoptim in the ‘DEoptim’ package.

Examples

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  simpleDE(fnTrefethen, lower = c(-1,-1), upper = c(1,1))
  # $fmin
  # [1] -3.306869
  # $xmin
  # [1] -0.02440308  0.21061243  # this is the true global optimum!